67.2k views
2 votes
Plant A: A graph has time (weeks) on the x-axis, and height (inches) on the y-axis. A line goes through points (0, 3), (1, 4.8), (2, 6.6), (3, 8.4). Plant B: A 2-column table with 3 rows. Column 1 is labeled Weeks with entries 2, 3, 4. Column 2 is labeled Height (inches) with entries 7.3, 8.7, 10.1. Simon claims that Plant B will be taller than Plant A in 6 weeks because it has the greater initial value. Is he correct? Yes. The plant with the greater initial value will continue to be taller. Yes. Plant B is 2.4 inches taller than Plant A at 6 weeks. No. The greater rate of change of Plant A will result in it being 0.9 inches taller in 6 weeks. No. The initial value of Plant A is greater.

2 Answers

2 votes

Answer:

No. The greater rate of change of Plant A will result in it being 0.9 inches taller in 6 weeks.

Explanation:

User Jurga
by
8.0k points
2 votes

Answer:

The correct option is;

No, The greater rate of change of Plant A will result in it being 0.9 inches taller in 6 weeks

Explanation:

The parameters given are;

Plant A:

Weeks, Height

0, 3

1, 4.8

2, 6.6

3, 8.4

The rate of change of height, H per week, t,
\left ((dH)/(dt) \right ) for plant A per week is therefore;


(dH)/(dt) = (H_n - H_((n-1)) )/(t_n - t_((n-1))) = (8.4 - 3 )/(3 - 0) = (5.4)/(3) = 1.8 \ inches/week

Therefore we have;

H = 1.8 × t + 3

At week 6,

H = 3 + 6×1.8 = 13.8 inches

Plant B

Weeks, Height

2, 7.3

3, 8.7

4, 10.1

The rate of change of height, H per week, t,
\left ((dH)/(dt) \right ) for plant B per week is given as follows;


(dH)/(dt) = (H_n - H_((n-1)) )/(t_n - t_((n-1))) = (10.1 - 7.3 )/(4 - 2) = (2.8)/(2) = 1.4 \ inches/week

Therefore we have;

When t = 2, H = 7.3 hence, 7.3 = 2 × 1.4 + H₀

Where:

H₀ = H at t = 0

H₀ = 7.3 - 2 × 1.4 = 4.5

At week 6 we have;

H = 4.5 + 6×1.4 = 12.9 inches

Which indicates that Plant A will be 0.9 inches taller than Plant B at week 6.

The correct option is therefore;

No, The greater rate of change of Plant A will result in it being 0.9 inches taller in 6 weeks.

User EliandroRibeiro
by
7.9k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories